Counting Zeros in Random Walks on the Integers and Analysis of Optimal Dual-Pivot Quicksort

Martin Aumüller, Martin Dietzfelbinger, Clemens Heuberger, Daniel Krenn, Helmut Prodinger

Research output: Conference Article in Proceeding or Book/Report chapterArticle in proceedingsResearchpeer-review

Abstract

We present an average case analysis of two variants of dual-pivot quicksort, one with a non-algorithmic
comparison-optimal partitioning strategy, the other with a closely related algorithmic strategy. For both
we calculate the expected number of comparisons exactly as well as asymptotically, in particular, we
provide exact expressions for the linear, logarithmic, and constant terms. An essential step is the analysis
of zeros of lattice paths in a certain probability model. Along the way a combinatorial identity is proven.
Original languageEnglish
Title of host publicationProceedings of the 27th Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
Number of pages13
PublisherJagiellonian University in Krakow
Publication date4 Jul 2016
Publication statusPublished - 4 Jul 2016
EventInternational Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms - Jagiellonian University, Kraków, Poland
Duration: 4 Jul 20167 Jul 2016
Conference number: 27
http://www.aofa2016.meetings.pl/

Conference

ConferenceInternational Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
Number27
LocationJagiellonian University
Country/TerritoryPoland
CityKraków
Period04/07/201607/07/2016
Internet address

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